Optimal designs for the identification of the order of a Fourier regression

For the Fourier regression model, we determine optimal designs for identifying the order of periodicity. It is shown that the optimal design problem for trigonometric regression models is equivalent to the problem of optimal design for discriminating between certain homo-and heteroscedastic polynomial regression models. These optimization problems are then solved using the theory of canonical moments, and the optimal discriminating designs for the Fourier regression model can be found explicitly. In contrast to many other optimality criteria for the trigonometric regression model, the optimal discriminating designs are not uniformly distributed on equidistant points.